1. Field of Invention
The present invention relates to the calculation of a current dipole from magnetic field measurements. More precisely, the present invention relates to improving the resolution of the inverse problem by defining more constraints than are available from the physically measured magnetic field.
2. Description of Related Art
Electric current source estimation is a common problem in various electromagnetic imaging technologies. For example, living organisms generate electric impulses, or electric fields, and electric imaging makes it possible to generate images of these electric fields. Electric imaging has found wide application in the medical field.
From physics, it is known that electric currents generate magnetic fields. Thus, organisms that generate electric impulses consequently also generate magnetic fields. The study of such magnetic fields in living organisms, or living tissues, is generally known as biomagnetism. The field of biomagnetism has been applied to the creation of magnetic images of the human brain and human heart.
The development of electric and magnetic imaging (or recording) technology permits the detection and analysis of electrophysiological processes in the brain, heart and other nerve systems. Recording/imaging of the electromagnetic fields from such tissues is typically accomplished by placing multiple electric or magnetic sensors around the tissue being studied. For example, electroencephalography (EEG) uses electric sensors placed around the brain to record electric images of brain tissue, and electrocardiography (ECG or EKG) uses electric sensors placed over the chest to record electric images of heart tissue. Similarly, magnetoencephalography (MEG) uses magnetic sensors placed around the brain to record magnetic images of brain tissue, and magnetocardiography (MCG) uses magnetic sensors placed over the chest to record magnetic images of heart tissue. Examples of an MEG unit and an MCG unit are provided in FIGS. 1A and 1B, respectively.
With reference to FIG. 1A, an MEG system consists of a large number (usually 300 or less) of magnetic sensors arranged in a spherical shape (to be fitted around a human head) to provide a high spatial resolution for measurements. The MEG system measures magnetic fields created by brain nerve activity. Each magnetic sensor measures a one-dimensional (1D) magnetic waveform, Bz, in the radial direction.
With reference to FIG. 1B, an MCG system may include a small number (normally 64 or fewer) of magnetic sensors (i.e. Superconducting Quantum Interference Devices, or SQUID arranged as a sensor planar array). Each SQUID sensor measures a 1D magnetic waveform (Bz) in the z direction, as illustrated by (x, y, z) axes. The MCG device is usually placed above and within 10 cm of a patient's chest in a location over the patient's heart. Electric current (i.e. electric impulse(s)) in the heart generates a magnetic field B that emanates out from the patient's torso. Each SQUID sensor measure the z-component (i.e. Bz) of the emanating magnetic field B that reaches it. That is, each SQUID sensor measures a 1D magnetic waveform in the z direction.
Compared to electric imaging (or recording) technology such as EEG and ECG, magnetic imaging technology such as MEG and MCG would be preferred due it being more non-invasive and providing a 2D image (by virtual of the x-y plane of SQUID sensors) at each time point. Moreover, the magnetic field generated outside of the human body is not distorted in the direction perpendicular to the body surface (e.g. the radial direction in FIG. 1A and the z-direction in FIG. 1B), due to the magnetic property of body tissue. Thus magnetic imaging is more accurate and sensitive to weak electric activity within the body.
By way of example, the following discussion focuses on magnetic imaging of heart tissue, but it is to be understood that the following discussion is also generally applicable to magnetic imaging and in particular applicable to magnetic imaging of other living tissues.
Cardiac electric currents (or current impulses) are generated by electrophysiological processes in the heart. Localization of abnormal electric currents may be used in the diagnosing of ischemic diseases such as myocardial infarction, angina cordis, etc. It also benefits patients in the catheter lab for both treatment and follow-up, as is explained in “Forty Years of Magnetocardiology”, by F. Stroink, in Int. Conf. on Biomagnetism Advances in Biomagnetism, 28:1-8, 2010.
Traditionally, irregular cardiac electric activity, such as arrhythmia, is diagnosed by means of an electrocardiogram (ECG). However, an ECG only provides temporal information, and thus cannot localize abnormal electric impulse currents in the heart directly, even if the ischemic disease has been detected. One technique to attempt to localize electrical impulse currents is known as Body Surface Potential Mapping (BSPM), which uses a large number of electrodes (i.e., leads) to reconstruct a body surface potential map. This BSPM technique is explained in “Noninvasive Volumetric Imaging of Cardiac Electrophysiology”, by Wang et al., in CVPR, pages 2176-2183, 2009. The accuracy of BSPM electric current localization, however, is limited because the observed electrical signals can be distorted by the poor conductivity of body tissue.
The advent of the magnetocardiogram, or magnetocardiography, (MCG) made available more accurate measurements of cardiac electric impulse currents, both spatially and temporally. An MCG is described above in reference to FIG. 1B.
In an MCG system, electromagnetic sensors (i.e. SQUID sensor) are arranged as a sensor planar array. Each electromagnetic sensor is a capture point, and hereinafter may be referred to as a “capture”. Each capture measures a one-dimensional (i.e. 1D) magnetic waveform in a direction perpendicular to the sensor planar array (i.e. the z-direction) emanating from the patient's chest (i.e. human torso). By aligning (or synchronizing) the depth measures (i.e. the 1D magnetic waveform) of the planar array of captures at a given depth in the z-direction (which may define an observation plane through the heart tissue), a two-dimensional (2D) MCG map at the given depth may be constructed. The MCG system is usually placed five to ten centimeters above the patient's chest 21, and measures the patient's heart magnetic field in a non-invasive manner. Thus, the array of captures measure a collection of low resolution (hereinafter, low-res), two-dimensional (2D) MCG maps of electromagnetic activity.
MCG has a few advantages over ECG. First, the magnetic field generated by the heart's electric current impulses (hereinafter, currents, electric currents or electrical currents) is not distorted in the direction perpendicular to the body surface (i.e., the z direction), due to the magnetic property of body tissue. Thus MCG is more accurate and sensitive to weak electric activity in the early stage of heart disorders. Second, the MCG sensor array can localize the position of electric currents in the heart. Finally, MCG measurements are non-invasive. After forty years of research in MCG, cardiac electric current localization and high resolution visualization for MCG measurements are attracting more and more interest from both research and clinical areas.
However, there are a number of difficulties associated with MCG. A first difficulty is the great amount of electromagnetic noise that can obscure the small magnetic fields created in a human heart. This has been addressed, to some extent, by using a magnetically-shielded room to reduce background noise and by the introduction of a sensitive electromagnetic sensor 13, such as the superconducting quantum interference device (SQUID). Although these steps have helped, the raw readings nonetheless remain more noisy than desired.
Another difficulty is the limited number of electromagnetic sensors (i.e. SQUIDs) that may be used in an MCG system, which limits the resolution of an MCG map. As a result, the MCG system can typically produce only low resolution (low-res) 2D MCG maps. Typically, these low-res 2D MCG maps are not sufficient for localizing electric currents in the heart. For example, a 64 channel Hitachi™ MCG system with a 25 mm sensor interval (as described in “Newly Developed Magnetocardiographic System for Diagnosing Heart Disease”, by Tsukada et al., in Hitachi Review, 50(1):13-17, 2001) only measures an 8×8 MCG map (i.e. an 8×8 array of 64 measurement points, or captures). One solution is to increase the number of sensors, but this is very difficult in practice due to the physical size of the sensors and system design.
An alternate approach is to approximate a high-res magnetic image from the low-res image created by the limited number of magnetic sensors. Thus, a necessary step in MCG is generating a high resolution (hereinafter high-res) 2D MCG image, or map, from a low-res 2D MCG image, or map. Two image examples L and R of high-res 2D MCG images are shown in FIG. 2. Left image L shows the tangential image of a generated high-res MCG image of a healthy heart. The maximal point (i.e. strongest point) within image L indicates the location (or source) of electric current in the heart. Thus, high-res MCG images permits doctors to directly “see” the electrical activity in the heart. Right image R shows the tangential image of a high-res MCG image of an unhealthy heart. It differs significantly from left image L of a healthy heart, and thus provides important cues for diagnosis. Compared to low-res MCG maps, high-res MCG images provide more diagnostic significance, and serve as the basis for an accurate electric current localization.
One way to generate a high-res magnetic field image from a low-res magnetic image is by interpolation. Most modern MCG systems use curve fitting interpolation methods between observed measurements of the electromagnetic sensors to construct high-res 2D MCG images from the low-res 2D MCG maps, such as described in “Magnetocardiographic Localization of Arrhythmia Substrates: A Methodology Study With Accessory Path-Way Ablation as Reference”, by B. A. S. et al., in Ann Noninvasive Electrocardiol, 10(2):152-160, 2005, and described in “Evaluation of an Infarction Vector by Magnetocardiogram: Detection of Electromotive Forces that Cannot be Deduced from an Electrocardiogram”, by Nomura et al, in Int. Congress Series, 1300:512-515, 2007. Unfortunately, the accuracy of curve fitting methods is typically limited.
Recently machine learning techniques have been used for high-res magnetic field image generation. An example is presented in Interpolation in MCG Mapping, IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China, pages 4381-4384, 2005, S. Jiang et al. This approach illustrates learning nonlinear interpolation functions using neural networks.
Another approach toward generating high-res magnetic images from low-res measurement images is to make use of the inverse problem, which attempts to identify the current impulse that generated an observed magnetic image. That is, using the obtained magnetic field measurements at different sites, one attempts to estimate the location and moment of the current source that generated the observed (i.e. the measured) magnetic field. This is called the inverse problem. For example, Conversion of Magnetocardiographic Recordings Between Two Different Multichannel Squid Devices, IEEE Trans. on Biomedical Engineering, 47(7):869-875, 2000, by M. B. et al. describes solving the inverse problem to reconstruct the 3D position, magnitude and orientation of current sources. Once the current source is known, the high-res magnetic field can be computed from the reconstructed current source by use of the Biot-Savart law. However, due to its poor initiation, this approach is often unreliable. Nonetheless, several approaches towards addressing the inverse problem have been proposed.
However, there are a number of difficulties involved in addressing the inverse problem. According to the Helmboltz reciprocity principal, the inverse problem for MCG is an ill-posed problem unless the prior electric currents and their number is known. For example, a trivia case that assumes a single electric current located at the world origin and far from the sensor array is described in Magnetocardiographic Localization of Arrhythmia Substrates: a Methodology Study with Accessory Pathway Ablation as Reference, Europace, 11(2):169-177, 2009, R. J. et al. This situation cannot be satisfied in practice.
In the case of estimating a large number of current sources, such as estimating nerve activity in the brain, the inverse problem can be put under constraints, such as describe in Magnetic Source Images Determined by a Lead-Field Analysis The Unique Minimum-Norm Least-Squares Estimation, IEEE Trans. Biomed Eng., 39(7):665-675, 1992, by J. Z. Wang et al. This approach requires solving a large scale non-linear optimization problem, which is often computationally expensive and may lead to undesired local optima without good initialization.
Alternatively, by considering the temporal information and signal-to-noise ratio, the inverse problem can by addressed by the beam-former and synthetic aperture magnetometery (SAM) methods, as described in MEG Inverse Problem with Leadfieds, 15th Japan Biomagnetism Conference, 13(1):42-45, 2000, by A. Matani. These type of methods require a statistical analysis of specific current sources, and thus does not permit the use of a one-time 2D magnetic field image without any assumptions on current sources.
Thus, addressing the inverse problem usually requires that it be simplified by making use of regularization methods (as described by Matani, above) and that the position of current sources be given by prior (as described in An Optimal Constrained Linear Inverse Method for Magnetic Source Imaging, Nuclear Science Symposium and Medical Imaging Conference, pages 1241-1245, 1993, by P. Hughett).
However, linear solutions to the inverse problem can be approximated in special cases where the current positions are fixed at uniform 3D grids, as put forth by J. Z. Wang et al. (cited above) and in Simulation Studies of Biomagnetic Computed Tomography, IEEE Trans. Biomed Eng., 40(4):317-322, 1993, C. Ramon et al.
C. Ramon et al. also show that the inverse problem can have over-constraints in the case of a single current source, which is popularly used in many applications of heart diseases diagnosis. But even in this case, the inverse problem is still a medium-scale nonlinear optimization process, which highly depends on the initialization and the number of independent constraints. However, the sparse magnetic measurement can only provide limited information for estimating good initialization and solving the inverse problem. For example, a 64-channel Hitachi MCG system only measures magnetic fields on an 8×8 grid with a 25 mm sensor interval.
What is needed is an MCG system that successfully further reduces the noise in observed low-res MCG maps.
Also needed is a method of better utilizing the high-res MCG maps to improve the observed measurements of an MCG system.